aiqbench analysis
This paper advances formal logic by defining three variants of Modus Tollens and counterfactual reasoning based on contradictory, opposite, and intermediary negations. While the work establishes rigorous truth value algorithms for these logical structures, it remains a theoretical contribution to symbolic AI rather than addressing practical machine learning models or quantum hardware. Consequently, its immediate relevance to the broader AI/quantum community is limited to foundational logic research without direct application implications.
Modus Tollens and Counterfactuals and Counterfactual Reasoning Based on Three Types of Negation
arXiv:2609.07483v1 Announce Type: new Abstract: Modus Tollens (MT) is a classical logical inference rule, while counterfactuals are hypothetical statements that are contrary to facts, and counterfactual reasoning is a process of reasoning based on counterfactuals. Negation is an indispensable core concept in them. In this paper, based on the logical systems LCOI&PLCOI with contradictory negation, opposite negation and intermediary negation, we propose three variants of Modus Tollens corresponding to distinct negation types, namely MTC: Modus Tollens based on contradictory negation, MTO: Modus Tollens based on opposite negation, and MTI: Modus Tollens based on intermediary negation. We define the implications within MTC, MTO and MTI, provide the truth value algorithms of MTC, MTO and MTI, and discuss the reducibility of these algorithms. To incorporate these three types of negation into counterfactuals and counterfactual reasoning, we differentiate counterfactuals into two types based on whether they possess logical negation, thereby proposing three counterfactuals and counterfactuals reasoning based on different logical negations. In this paper, we further argue that the three counterfactuals reasoning based on different logical negations have the same inference form as MTC, MTO and MTI, respectively. In other words, they share the same inference structure. As a result, the truth value algorithms for MTC, MTO and MTI can be as the truth value algorithms for the three counterfactuals reasoning based on different logical negations. The algorithms indicates that if the first premise of the reasoning is true, the truth values of the reasoning conclusions are identical to the truth values of the three negative premises in the reasoning premises, respectively. This reflects the consistency and accuracy of the truth value algorithms.
Abstract:Modus Tollens (MT) is a classical logical inference rule, while counterfactuals are hypothetical statements that are contrary to facts, and counterfactual reasoning is a process of reasoning based on counterfactuals. Negation is an indispensable core concept in them. In this paper, based on the logical systems LCOI&PLCOI with contradictory negation, opposite negation and intermediary negation, we propose three variants of Modus Tollens corresponding to distinct negation types, namely MTC: Modus Tollens based on contradictory negation, MTO: Modus Tollens based on opposite negation, and MTI: Modus Tollens based on intermediary negation. We define the implications within MTC, MTO and MTI, provide the truth value algorithms of MTC, MTO and MTI, and discuss the reducibility of these algorithms. To incorporate these three types of negation into counterfactuals and counterfactual reasoning, we differentiate counterfactuals into two types based on whether they possess logical negation, thereby proposing three counterfactuals and counterfactuals reasoning based on different logical negations. In this paper, we further argue that the three counterfactuals reasoning based on different logical negations have the same inference form as MTC, MTO and MTI, respectively. In other words, they share the same inference structure. As a result, the truth value algorithms for MTC, MTO and MTI can be as the truth value algorithms for the three counterfactuals reasoning based on different logical negations. The algorithms indicates that if the first premise of the reasoning is true, the truth values of the reasoning conclusions are identical to the truth values of the three negative premises in the reasoning premises, respectively. This reflects the consistency and accuracy of the truth value algorithms.
Artificial Intelligence (cs.AI)
arXiv:2609.07483 [cs.AI]
(or arXiv:2609.07483v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2609.07483 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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